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The general form for the equation of a circle centre (xo, yo) and radius r is:

(x - xo)2 + (y - yo)2 = r2

Which can be rearranged into:

x2 - 2xox + y2 - 2yoy = r2 - xo2 - yo2

So a circle with centre (4, -1) and radius 8 has equations:

(x - 4)2 + (y + 1)2 = 64

x2 - 8x + y2 + 2y = 47

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